Given the problems that our global climate models have in simulating the global mean energy balance of the Earth, some readers may have a hard time understanding why many of us in climate science devote so much attention to these models. A big part of the explanation is the quality of the large-scale atmospheric circulation that they provide. To my mind this is without doubt one of the great triumphs of computer simulation in all of science.

The figure above is meant to give you a feeling for this quality. It shows the zonal (eastward) component of the wind as a function of latitude and pressure, averaged in time and around latitude circles. This is an atmosphere/land model running over observed ocean temperatures with roughly 50km horizontal resolution. The model results at the top (dec-jan-feb on the left and june-july-aug on the right) are compared with the observational estimate below them. The observations are provided by a reanalysis product(more on reanalysis below). The contour interval is 5m/s; westerlies (eastward flow) are red, easterlies are blue. Features of interest are the location of the transition from westerlies to easterlies at the surface in the subtropics, and the relative positions of the the subtropical jet at 200mb, the lower tropospheric westerlies and the polar stratospheric jet in winter (the latter is barely visible near the upper boundary of the plot when using pressure as a vertical coordinate).

Fig. 9.8 from the AR5 Working Group 1 IPCC report. Global mean surface temperatures simulated by a set of climate models, shown as anomalies from the time mean over a reference period 1961-1990. Observations (HADCRUT4) in black; ensemble mean in red. On the right (circled) are the mean temperatures in the reference period.

Ch.9 of the AR5-WG1 report, “Evaluating Climate Models” is, in my opinion, the most difficult to write of any chapter in that report. You can think of hundreds if not thousands of interesting ways of comparing modern climate models to observations, but which of these is the most relevant for judging the quality of a projection for a particular aspect of climate change over the next century? This is an important research problem. Consider this figure, which shows the familiar simulated changes in global mean surface temperature over the past 150 years, in a set of models deposited in the CMIP5 archive, as anomalies from the model’s own temperature during some reference period (shaded). But the figure also shows in the narrow panel on the right side, circled in red, the models’ mean temperatures during that reference period. People tend to be disappointed when they see this — some models are better than others but the biases in the model’s global mean temperature are typically comparable to the 20th century warming and in some cases larger. If we are interested in projections of global mean warming over the coming century, or in the attribution of this past warming, should we trust these models at all, given these biases?

Traditional “lapse rate feedback” in CMIP3 models, over the 21st century in the A1B scenario, plotted against the degree of polar amplification of surface warming in those models (tropical – 30S-30N divided by global mean warming). From Soden and Held 2006.

“Everything should be made as simple as possible, but not simpler.” There is evidently no record of Einstein having actually used these words , and a quote of his that may be the source of this aphorism has a somewhat different resonance to my ear. In any case, I want to argue here that thinking about the global mean temperature in isolation or working with simple globally averaged box models that ignore the spatial structure of the response is very often “too simple”. I am reiterating some points made in earlier posts, especially #5, #7, and #44, but maybe it is useful to gather these together for emphasis.

This animation is the response of a two-dimensional flow on the surface of a rotating sphere to a source that mimics stationary localized heating centered on the equator. The top panel is a north-south component of the wind — red is northward and blue southward. The bottom panel is the streamfunction of the flow –lines of constant streamfunction are the trajectories of fluid particles once the flow becomes steady. At the start of the animation the flow is purely zonal and the forcing is turned on instantaneously and then maintained. The loop covers about 40 days, but the pattern is fully set up in less than half that time. The continental outlines are just meant to help orient the viewer; the surface in this model is featureless. The setup is a classical one for generating a stationary Rossby wave propagating from the tropics into midlatitudes described by Brian Hoskins and colleagues in the late 1970′s and early 80′s (Hoskins et al 1977; Hoskins and Karoly 1981). This kind of wave is the essence of the teleconnections that atmospheric scientists talk about so frequently — patterns of flow that connect widely separated regions. Sometimes the correlations introduced into climate time series by these remotely forced responses can seem like spooky action-at-a-distance. But nothing could be further from the truth. They are just Rossby waves at heart.

Multi-model median of changes in near surface a) temperature, b) relative humidity, and c) equivalent potential temperature between the historical simulation (1975-2004) and the RCP8.5 (2079-2099) simulations in CMIP5. From Byrne and O’Gorman 2013.

In global warming simulations the surface air over land warms more than over the oceans in the tropics, while the relative humidity decreases over land, increasing a bit over the oceans, as illustrated in panels a) and b) above from a recent paper by Michael Byrne and Paul O’Gorman. A quantity that is relevant for the convective instability of the atmosphere and the profile of temperature on a rising air parcel is the equivalent potential temperature, . Strikingly the increase in is quite uniform in the deep tropics, irrespective of whether the underlying surface is land or ocean. This is not an accident and provides us with a simple way of thinking about increasing heat stress with warming.

Vertical profile of temperature trends averaged over 20S-20N in two models. Solid: trends in a 30-year (1970-2000) realization of the CM2.1 coupled model using estimated forcing agents from 1970-2000. Dashed: simulation using the atmosphere/land component of CM2.1 with the same forcing agents but running over the sea surface temperatures generated in this realization of the coupled model.

The previous post summarizes the results from a recent paper, Flannaghan et al 2014, that uses atmosphere/land models running over observed sea surface temperatures (SSTs) to look at the consistency between these models and observations of tropical tropospheric temperature trends. The idea of using this kind of uncoupled model is to try to put aside the issue of SST trends in the tropics and focus more sharply on the vertical structure of the temperature trends. Because models are so consistent in producing a warming trend that is top-heavy in the tropical troposphere, due to the strong tendency to follow a moist adiabatic profile, and because this pattern of change has numerous ramifications for tropical climate more generally, any possibility that this warming profile is wrong takes precedence over other issues in tropical climate change, in my view. I interpret the results in Flannaghan et al to say that microwave sounding data, at least, does not require us to reject the hypothesis provided by climate models for the vertical profile of the tropical temperature trends.

To follow up on the last post, I would like to discuss, or at least mention, some other issues regarding this setup, in which SSTs are simply prescribed as a boundary condition. Could there be something fundamentally flawed about this approach? This may seem like a technical issue, but a large fraction of atmospheric model development takes place in this prescribed SST framework to try to separate biases due to atmospheric model imperfections from those due to the ocean/sea ice model, so it is important to understand its limitations. I have used this kind of setup in a number of posts to address other issues, for example #2,#10, #11, #32, #34; any limitations to this decoupled framework could affect my own thinking about a variety of climate change issues.

Mid-tropospheric temperature trends (TTT channel — see below) from a given start date till 2008, plotted as a function of start date, in three analyses of the MSU data (thin lines) and in an atmosphere/land model running over two estimates of observed sea surface temperatures: HadISST1 (blue), Hurrell (red). The upper panel is the trend from ordinary least squares while the lower panel uses the Theil-Sen estimator.

In a paper just published, Flannaghan et al 2014, my colleagues (Tom Flannaghan, Stephan Fueglistaler, Stephen Po-Chedley, Bruce Wyman, and Ming Zhao) and I have returned to the question of tropical tropospheric warming in models and observations — Microwave Sounding Unit (MSU) observations specifically. This work was motivated in part (in my mind at least) by the material in Post #21, but the results have evolved significantly. All the figures in this post are from the Flannaghan et al paper.

There are important discrepancies between models and observations regarding tropical tropospheric temperature trends. It is informative if we can divide these into two parts, one associated with the sea surface temperature (SST) trends and the other with the vertical structure of the trends in the atmosphere and how these trends are related to the SST trends. The former is associated with issues of climate sensitivity and internal variability; the latter is related to the internal dynamics of the atmosphere, especially the extent to which the vertical structure of the temperature profile is controlled by the moist adiabat. A moist adiabatic temperature profile is what you get by raising a parcel which then cools adiabatically due to expansion, with part of this cooling offset by the warming due to the latent heat released when the water vapor in the parcel condenses. The tropical atmosphere is observed to lie close to this profile, as do our models. Models continue to approximately follow this profile as they warm., so they invariably produce larger warming in the upper troposphere than at the surface in the tropics — simply because the water vapor in the parcel increases with warming, so there is more heating due to condensation as the parcel rises. All models do this, from global models to idealized “cloud resolving” models with much finer resolution — see Post #20 for a discussion of the latter. The same top-heaviness is seen in the tropospheric temperature changes accompanying ENSO variability, which models simulate very well. Why should lower frequency trends behave any differently than the year-to-year variability resulting from ENSO? If models have this wrong it has a lot of implications.

Magnitude of eastward winds in the upper troposphere in the “fruit fly” model using the Earth’s rotation rate (bottom) and using a rotation rate that is 4 times larger (top). The red saturates at 50m/s eastward flow in the lower panel and 30 m/s in the upper panel. (Lat-lon plot over the entire globe — 50 Earth days of simulation in each clip.)

In post 28, I described a model of an ideal gas atmosphere with no latent heat (no water vapor for that matter) with radiative heating/cooling a function of temperature only, with no seasonal cycle, and with linear drag near the surface relaxing the flow back to zero in a rotating reference frame (this is how the atmosphere knows that it is rotating). The lower boundary condition is a homogeneous spherical surface (no mountains, no continents, no oceans). I think of this model as part of a hierarchy of models of increasing complexity so with an admiring reference to the way in which biological research is organizing around “model” organisms I refer to this as the “fruit fly” model. In that post, I mentioned that the surface westerlies move polewards as the rotation rate is decreased. Poleward movement of the westerlies is what we expect in a warming world. There is no guarantee that what we learn by varying the rotation rate in this very controlled setting will be directly relevant to that problem but I think it does stress our understanding in interesting ways . The animation above compares the evolution of the zonal (east-west) component of the wind in the upper troposphere when using the Earth’s rotation rate with the evolution you get with 4 times the Earth’s rotation rate.

Fractional change in global mean precipitation (blue) and global mean (horizontally and vertically integrated) water vapor (red) as a function of change in global mean surface air temperature, over the 21st century in the A1B scenario in CMIP3 models. Redrawn from fig. 2 in Held and Soden 2006.

The figure at the top describes a very robust result in the responses to warming in global climate models: the fractional increase in the total amount of water vapor in the atmosphere is much larger than the fractional increase in global mean precipitation. While this figure shows the responses in CMIP3 models for a particular scenario of increasing forcing over the 21st century, the results from CMIP5 and different scenarios are all similar. This disparity in the magnitude of the increases in water vapor and precipitation and its important consequences for many other aspects of the climate response have been discussed since relatively early days in GCM simulations of climate change (e.g., Mitchell et al 1987). Perhaps the most fundamental consequence is the reduction in the vertical mass exchange between the lower and upper troposphere. That is, the “amount of convection” in the atmosphere decreases — or, by this particular measure, the atmospheric circulation slows down, especially in the tropics where a large fraction of this exchange takes place.

Vertical diffusion of heat has often been used as a starting point for thinking about ocean heat uptake associated with forced climate change. I have chosen instead to use simple box models for this purpose in these posts because they are easier to manipulate but also because I don’t feel that the simplest diffusive models bring you much closer to the underlying ocean dynamics. But diffusion does provide a simple way of capturing the qualitative idea that deeper layers of the ocean, and larger heat capacities, become involved more or less continuously as the time scales increase. So let’s take a look at the simplest possible diffusive model for the global mean temperature response. This model is typically embellished with a surface box, representing the ocean mixed layer, as well as by some attempt at capturing advective rather than diffusive transport (ie Hoffert, et al 1980, and Wigley and Schlesinger 1985), but let’s not worry about that. I want to use this model to make a simple point about the value of the concept of the transient climate response (TCR).